Erratum: Degenerate diffusion with a drift potential: A viscosity solution approach

TL;DR

This paper corrects a previous result on degenerate diffusion with a drift potential, clarifying the valid parameter range for convergence estimates and providing partial results for the case when the permeability constant exceeds 2.

Contribution

It identifies and corrects an error in earlier work, establishing accurate convergence bounds for the diffusion equation within specific parameter ranges.

Findings

Validates convergence estimates for 1<m<2

Provides partial convergence results for m≥2

Clarifies the limitations of previous bounds

Abstract

The earlier paper [LK] (arXiv:0910.3432) contains a lower bound of the solution in terms of its $L^1$ norm, which is incorrect. In this note we explain the mistake and present a correction to it under the restriction that the permeability constant $m$ satisfies $1< m <2$. As a consequence, the quantitative estimates on the convergence rate (Main Theorem (c) and Theorem 3.6 in [LK] only hold for $1<m<2$. For $m\geq 2$ a partial convergence rate is obtained.